Skip to main content
SpringerLink
Log in

BUNDLE: A Reasoner for Probabilistic Ontologies

  • Conference paper
Web Reasoning and Rule Systems (RR 2013)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7994))

Included in the following conference series:

Abstract

Representing uncertain information is very important for modeling real world domains. Recently, the DISPONTE semantics has been proposed for probabilistic description logics. In DISPONTE, the axioms of a knowledge base can be annotated with a set of variables and a real number between 0 and 1. This real number represents the probability of each version of the axiom in which the specified variables are instantiated. In this paper we present the algorithm BUNDLE for computing the probability of queries from DISPONTE knowledge bases that follow the \(\mathcal{ALC}\) semantics. BUNDLE exploits an underlying DL reasoner, such as Pellet, that is able to return explanations for queries. The explanations are encoded in a Binary Decision Diagram from which the probability of the query is computed. The experiments performed by applying BUNDLE to probabilistic knowledge bases show that it can handle ontologies of realistic size and is competitive with the system PRONTO for the probabilistic description logic P-\(\mathcal{SHIQ}\)(D).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press (2003)

    Google Scholar 

  2. Baader, F., Horrocks, I., Sattler, U.: Description logics. In: Handbook of Knowledge Representation, ch. 3, pp. 135–179. Elsevier (2008)

    Google Scholar 

  3. Bellodi, E., Riguzzi, F.: Experimentation of an expectation maximization algorithm for probabilistic logic programs. Intelligenza Artificiale 8(1), 3–18 (2012)

    Google Scholar 

  4. Bellodi, E., Riguzzi, F.: Expectation Maximization over binary decision diagrams for probabilistic logic programs. Intel. Data Anal. 17(2), 343–363 (2013)

    Google Scholar 

  5. Bollig, B., Wegener, I.: Improving the variable ordering of OBDDs is NP-complete. IEEE Trans. Computers 45(9), 993–1002 (1996)

    Article  MATH  Google Scholar 

  6. Calvanese, D., Lenzerini, M.: On the interaction between isa and cardinality constraints. In: International Conference on Data Engineering, pp. 204–213. IEEE Computer Society (1994)

    Google Scholar 

  7. Darwiche, A., Marquis, P.: A knowledge compilation map. J. Artif. Intell. Res. 17, 229–264 (2002)

    MathSciNet  MATH  Google Scholar 

  8. De Raedt, L., Kimmig, A., Toivonen, H.: ProbLog: A probabilistic Prolog and its application in link discovery. In: International Joint Conference on Artificial Intelligence, pp. 2462–2467 (2007)

    Google Scholar 

  9. Grumberg, O., Livne, S., Markovitch, S.: Learning to order BDD variables in verification. J. Artif. Intell. Res. 18, 83–116 (2003)

    MathSciNet  MATH  Google Scholar 

  10. Horridge, M., Parsia, B., Sattler, U.: Explaining inconsistencies in OWL ontologies. In: Godo, L., Pugliese, A. (eds.) SUM 2009. LNCS, vol. 5785, pp. 124–137. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Kalyanpur, A.: Debugging and Repair of OWL Ontologies. Ph.D. thesis, The Graduate School of the University of Maryland (2006)

    Google Scholar 

  12. Kalyanpur, A., Parsia, B., Horridge, M., Sirin, E.: Finding all justifications of OWL DL entailments. In: Aberer, K., et al. (eds.) ISWC/ASWC 2007. LNCS, vol. 4825, pp. 267–280. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Kimmig, A., Demoen, B., De Raedt, L., Costa, V.S., Rocha, R.: On the implementation of the probabilistic logic programming language ProbLog. Theor. Prac. Log. Prog. 11(2-3), 235–262 (2011)

    Article  MATH  Google Scholar 

  14. Klinov, P.: Pronto: A non-monotonic probabilistic description logic reasoner. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 822–826. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Klinov, P., Parsia, B.: Optimization and evaluation of reasoning in probabilistic description logic: Towards a systematic approach. In: Sheth, A., Staab, S., Dean, M., Paolucci, M., Maynard, D., Finin, T., Thirunarayan, K. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 213–228. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Int. 172(6-7), 852–883 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the semantic web. J. Web Sem. 6(4), 291–308 (2008)

    Article  Google Scholar 

  18. Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–87 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  19. Patel-Schneider, P.F., Horrocks, I., Bechhofer, S.: Tutorial on OWL (2003)

    Google Scholar 

  20. Poole, D.: The Independent Choice Logic for modelling multiple agents under uncertainty. Artif. Intell. 94(1-2), 7–56 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  21. Rauzy, A., Châtelet, E., Dutuit, Y., Bérenguer, C.: A practical comparison of methods to assess sum-of-products. Reliability Engineering and System Safety 79(1), 33–42 (2003)

    Article  Google Scholar 

  22. Riguzzi, F.: Extended semantics and inference for the Independent Choice Logic. Log. J. IGPL 17(6), 589–629 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Riguzzi, F., Bellodi, E., Lamma, E., Zese, R.: Parameter learning for probabilistic ontologies. In: Faber, W., Lembo, D. (eds.) RR 2013. LNCS, vol. 7994, pp. 265–270. Springer, Heidelberg (2013)

    Google Scholar 

  24. Riguzzi, F., Bellodi, E., Lamma, E., Zese, R.: Epistemic and statistical probabilistic ontologies. In: Uncertainty Reasoning for the Semantic Web. CEUR Workshop Proceedings, vol. 900, pp. 3–14. Sun SITE Central Europe (2012)

    Google Scholar 

  25. Sato, T.: A statistical learning method for logic programs with distribution semantics. In: International Conference on Logic Programming, pp. 715–729. MIT Press (1995)

    Google Scholar 

  26. Sato, T., Kameya, Y.: Parameter learning of logic programs for symbolic-statistical modeling. J. Artif. Intell. Res. 15, 391–454 (2001)

    MathSciNet  MATH  Google Scholar 

  27. Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: International Joint Conference on Artificial Intelligence, pp. 355–362. Morgan Kaufmann (2003)

    Google Scholar 

  28. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artif. Intell. 48(1), 1–26 (1991)

    Article  MATH  Google Scholar 

  29. Sirin, E., Parsia, B., Cuenca-Grau, B., Kalyanpur, A., Katz, Y.: Pellet: A practical OWL-DL reasoner. J. Web Sem. 5(2), 51–53 (2007)

    Article  Google Scholar 

  30. Straccia, U.: Managing uncertainty and vagueness in description logics, logic programs and description logic programs. In: Baroglio, C., Bonatti, P.A., Małuszyński, J., Marchiori, M., Polleres, A., Schaffert, S. (eds.) Reasoning Web 2008. LNCS, vol. 5224, pp. 54–103. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  31. Valiant, L.G.: The complexity of enumeration and reliability problems. SIAM J. Comp. 8(3), 410–421 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  32. Vennekens, J., Verbaeten, S., Bruynooghe, M.: Logic programs with annotated disjunctions. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 431–445. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, University of Ferrara, Via Saragat 1, I-44122, Ferrara, Italy

    Fabrizio Riguzzi

  2. Dipartimento di Ingegneria, University of Ferrara, Via Saragat 1, I-44122, Ferrara, Italy

    Elena Bellodi, Evelina Lamma & Riccardo Zese

Authors
  1. Fabrizio Riguzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elena Bellodi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Evelina Lamma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Riccardo Zese
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Calabria, Via P. Bucci, cubo 30b, 87036, Rende, Italy

    Wolfgang Faber

  2. Department of Computer, Control, and Management Engineering Antonio Ruberti, Sapienza University of Rome, Via Ariosto, 25, 00185, Roma, Italy

    Domenico Lembo

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Riguzzi, F., Bellodi, E., Lamma, E., Zese, R. (2013). BUNDLE: A Reasoner for Probabilistic Ontologies. In: Faber, W., Lembo, D. (eds) Web Reasoning and Rule Systems. RR 2013. Lecture Notes in Computer Science, vol 7994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39666-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39666-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39665-6

  • Online ISBN: 978-3-642-39666-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation